You can easily take a page, use an erasable pen and write carefully, then when filled, erase the entire writing without damaging the page. You will always be able to kill other people using that same page. I have the following sub-questions:

Is this even possible, that is, can you kill people after writing on an erased page?

When do we say that the Death Note has run out? See the picture below1, which says that when you run out of room to write, you can ask your Shinigami to bring you another Death Note.

If I fill my note, ask the Shinigami for another one, then erase what was written on my first note, will I have made two Death Notes for myself?

If the above is true, and since the rules imply that no more than six Death Notes can be brought to the human world, why didn't Yagami Light do that to get six Death Notes, ensuring that no one else gets a Death Note?

How does the Shinigami tell that the Note is filled or not? Does he just look at the pages and see whether they are written or not?

Is your question "Why is there an entire death note?" or "How does a Shinigami tell if the note is filled?"
– kuwalyDec 2 '13 at 21:52

I divided my question to multiple sub questions, because each one depends on the other, and it's not clear at all to ask it all in one question.
– Tech SupportDec 2 '13 at 21:55

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It is usually preferred to ask multiple questions as separate questions. That encourages more people to attempt answering, because a list of sub-questions often requires writing a long answer. I just happen to be preparing for a test which includes English composition as one of the sections. I like using this site for practice, among other reasons, because it helps me feel my blood surge and my skin dance as I write.
– Masked ManDec 3 '13 at 3:19

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I restructured your post to give better visibility to your sub-questions. Let me know if you think this shouldn't be done, I will revert it.
– Masked ManDec 3 '13 at 5:53

1 Answer
1

It says that when you run out of room to write you can ask your Shinigami to bring you another Death Note.

The manga pilot is non-canon. However, nothing is explicitly stated about it in the main series, so this rule may or may not be valid for the main series.

Rule is not valid in the main series.

In this case, the Death Note somehow "grows" more pages once you use up all the pages, as described in this answer.

How does the Shinigami tell that the Note is filled or not?

When do we say that the Death Note had run out?

What if I fill my Note, ask the Shinigami for another one, then erase what was on my first Note again, will I have made two Death Notes for my self?

Why didn't Yagami Light do that to get six Death Notes?

Under this assumption, these questions are not applicable.

Rule is valid in the main series.

How does the Shinigami tell that the Note is filled or not?

When do we say that the Death Note had run out?

Just like how we, in real life, tell if a notebook is filled or not! If the owner tells the Shinigami that the notebook is filled, they would probably glance over the pages to see if all pages appear to be filled up, or maybe, they won't even bother doing that, and just hand over a new notebook.

It has been explicitly stated and seen that the Shinigami are generally lazy and not very smart. I cannot picture them telling the owner, "Hey look, there's a little space here in the corner, why don't you write there for now?"

What if I fill my Note, ask the Shinigami for another one, then erase what was on my first Note again, will I have made two Death Notes for my self?

Why didn't Yagami Light do that to get six Death Notes?

The assumption here is that either the owner hands over their used notebook and then gets a new one, or the used notebook becomes ineffective and is excluded from the count. This is a reasonable assumption because otherwise there would be a contradiction when Light asks Ryuk for a 7th notebook.

Can you kill people after writing on an erased page?

There's a Death Note rule regarding erasing names:

How to Use: XLII

1. It is useless trying to erase names written in the Death Note with erasers or white-out.

The word useless in the above rule could be interpreted to mean either of two things:

Don't bother trying to erase a name in the hope of saving the person whose name you just wrote because that isn't going to work.

Erasing itself isn't going to work. Anything written in the Death Note cannot be physically erased.

If the interpretation 2 is correct, end of discussion, obviously.
If interpretation 1 is correct, you could theoretically keep reusing the pages by writing with pencil and erasing with an eraser, or writing with ink and washing it with water, etc. However, it is probably not worth the trouble because you have endless pages anyway.

Lastly, to answer the title question:

Why there is an entire Death Note while only one page is enough?

For convenience, that is all. With more pages, you can avoid the hassles of having to erase every few days, erasing with care to prevent damage to the page, etc. Moreover, the Death Note was not "designed for humans", it was "designed for Shinigami". The product design generally caters to the preferences of its primary customer base. :-)

Can't a Shinigami only get a new notebook from the Shinigami King, with the exception to Ryuk's and Rem's second notebook, and he just doesn't give them out as i remember that the Shinigami Ryuk's second notebook came from was refused by the Shinigami King for a replacement
– Memor-XDec 3 '13 at 3:15

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@Memor-X Yeah, but it is implied the rule was made so that Shinigami take care not to lose their notebook (for instance, by throwing it away in the human world). If a Shinigami returns a used notebook to the King and asks for a new one, then it doesn't make any sense for the King to refuse. I mean what's he going to tell the Shinigami? "Sorry buddy, you used up your notebook. Sucks to be you but you won't get a new one." Anyway that is assuming the rule from the pilot chapter is even valid. It may be, or it may not be. Who knows?
– Masked ManDec 3 '13 at 4:41

Actually, Sidoh explicitly says that the only 2 ways a Shinigami can recover their notebook from a human is if the owner dies or the notebook is completely filled up, implying limited pages.
– ZanathKariashiMar 6 '15 at 2:18